Questions 1 to 22 carry 3 marks each.

7 A contractor hired a group of workers to do a job in 3 days. But due to poor work conditions, 8 workers dropped out every day, and hence the job could be completed only at the end of the 5th day. Initially how many workers were hired by the contractor?

1) 45

2) 40

3) 48

4) 36

Let the initial number of workers hired by the contractor be \( x \).

The job was supposed to be completed in 3 days. Therefore, the total work is equivalent to \( 3x \) worker-days (i.e., the total amount of work that needs to be done is \( 3 \times x \) workers working for 3 days).

However, because 8 workers dropped out each day, the job was completed in 5 days instead. Let's calculate the number of workers available each day:

- On Day 1, there are \( x \) workers.
- On Day 2, 8 workers dropped out, so there are \( x - 8 \) workers.
- On Day 3, 8 more workers dropped out, so there are \( x - 16 \) workers.
- On Day 4, 8 more workers dropped out, so there are \( x - 24 \) workers.
- On Day 5, 8 more workers dropped out, so there are \( x - 32 \) workers.

The total work done over the 5 days can be calculated as the sum of the number of workers each day:

\[
\text{Total work} = x + (x - 8) + (x - 16) + (x - 24) + (x - 32)
\]

Simplifying this expression:

\[
\text{Total work} = 5x - (8 + 16 + 24 + 32)
\]
\[
\text{Total work} = 5x - 80
\]

Since the total amount of work is the same, we equate this to the original work, \( 3x \):

\[
5x - 80 = 3x
\]

Solving for \( x \):

\[
5x - 3x = 80
\]
\[
2x = 80
\]
\[
x = 40
\]

Thus, the initial number of workers hired by the contractor is \( \boxed{40} \).

Would you like more details or have any questions?  
Here are some related questions for practice:

1. If 10 workers dropped out every day, how many workers were initially hired?
2. What if the job was supposed to be done in 4 days but took 6 days instead?
3. If the job took 7 days due to 5 workers dropping out daily, how many were initially hired?
4. How does increasing the daily dropout rate affect the total number of days?
5. Can you express the total work in terms of \( n \), where \( n \) is the number of days the job took?

**Tip:** Breaking down word problems into smaller steps helps simplify the solution.

A contractor hired a group of workers to do a job in 3 days. But due to poor work conditions, 8 workers dropped out every day, and hence the job could be completed only at the end of the 5th day. Initially how many workers were hired by the contractor?

1) 45
2) 40
3) 48
4) 36

This work and time problem involves calculating the initial number of workers hired by a contractor when 8 workers drop out daily over a 5-day period. Detailed step-by-step algebraic solution provided. Ideal for students in Grades 9-11.

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